The discovery that tumor cells release tumor-derived DNA into the blood stream has sparked the development of non-invasive methods capable of determining the presence, location and/or type of tumor in a subject using cell-free samples (e.g., plasma). Many tumors can be treatable if detected early in their development. However, current methods can lack the sensitivity and/or specificity to detect a tumor at an early stage and can return a large number of false positive or false negative results. The sensitivity of a test can refer to the likelihood that a subject that is positive for a condition tests positive for the condition. The specificity of a test can refer to the likelihood that a subject that is negative for a condition tests negative for that condition. The problems of sensitivity and specificity can be exaggerated in assays for the early detection of tumors, e.g., because samples on which such tumor detection methods are performed can have relatively small amounts of tumor-derived DNA and because the condition itself can have a relatively low prevalence among individuals tested in the early stage. Accordingly, there is a clinical need for methods having higher sensitivity and/or specificity for the detection of tumors.